Problem: Rewrite as a simplified fraction. ${0.\overline{70} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 70.707...\\ 1x &= 0.707...\end{align*}}$ Subtracting the two equations, we have: ${99x = 70}$ ${x = \dfrac{70}{99}} $